Abstract

Using terahertz near-field imaging we experimentally investigate the resonant electromagnetic field distributions behind a split-ring resonator and its complementary structure with sub-wavelength spatial resolution. For the out-of-plane components we experimentally verify complementarity of electric and magnetic fields as predicted by Babinet’s principle. This duality of near-fields can be used to indirectly map resonant magnetic fields close to metallic microstructures by measuring the electric fields close to their complementary analogues which is particularly useful since magnetic near-fields are still extremely difficult to access in the THz regime. We find excellent agreement between the results from theory, simulation and two different experimental near-field techniques.

© 2011 OSA

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2010 (3)

2009 (3)

2008 (4)

2007 (5)

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15, 1084–1095 (2007).
[Crossref] [PubMed]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15, 11781–11789 (2007).
[Crossref] [PubMed]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).
[Crossref]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref] [PubMed]

2005 (2)

P. C. M. Planken, C. E. W. M. van Rijmenam, and R. N. Schouten, “Opto-electronic pulsed THz systems,” Semicond. Sci. Technol. 20, S121–S127 (2005).
[Crossref]

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

2004 (2)

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

2002 (2)

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[Crossref]

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

1997 (1)

M. Osawa, “Dynamic processes in electrochemical reactions studied by surface-enhanced infrared absorption spectroscopy (seiras),” Bull. Chem. Soc. Jpn. 70, 2861–2880 (1997).
[Crossref]

1990 (1)

Adam, A. J. L.

Ahn, K. J.

Al-Naib, I. A. I.

I. A. I. Al-Naib, C. Jansen, and M. Koch, “Applying the Babinet principle to asymmetric resonators,” Electron. Lett. 44, 1228–1229 (2008).
[Crossref]

Averitt, R. D.

Baena, J. D.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Beruete, M.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Bitzer, A.

Bonache, J.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Brok, J. M.

Burresi, M.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Chen, C. C.

Chen, H. T.

Falcone, F.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Fattinger, C.

Fedotov, V. A.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

Feurer, T.

Garcia-Garcia, J.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

Giessen, H.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Gil, I.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

Grischkowsky, D.

Heideman, R.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Helm, H.

Highstrete, C.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Jansen, C.

I. A. I. Al-Naib, C. Jansen, and M. Koch, “Applying the Babinet principle to asymmetric resonators,” Electron. Lett. 44, 1228–1229 (2008).
[Crossref]

Jeoung, S. C.

Kaiser, S.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Kalinin, V. A.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002).
[Crossref]

Kampfrath, T.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Kang, J. H.

Keiding, S.

Kim, D. S.

Koch, M.

I. A. I. Al-Naib, C. Jansen, and M. Koch, “Applying the Babinet principle to asymmetric resonators,” Electron. Lett. 44, 1228–1229 (2008).
[Crossref]

Kuipers, L.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Kuo, P.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

Laso, M. A. G.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Lederer, F.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Lee, J. W.

Lee, M.

Leinse, A.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref] [PubMed]

Lopetegi, T.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Marques, R.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

Martin, F.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Merbold, H.

Meyrath, T. P.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Nagel, M.

O’Hara, J. F.

Ortner, A.

Osawa, M.

M. Osawa, “Dynamic processes in electrochemical reactions studied by surface-enhanced infrared absorption spectroscopy (seiras),” Bull. Chem. Soc. Jpn. 70, 2861–2880 (1997).
[Crossref]

Padilla, W. J.

Papasimakis, N.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

Park, Q. H.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Planken, P. C. M.

Plum, E.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

Portillo, M. F.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

Ringhofer, K. H.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002).
[Crossref]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Rockstuhl, C.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Schoenmaker, H.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Schouten, R. N.

P. C. M. Planken, C. E. W. M. van Rijmenam, and R. N. Schouten, “Opto-electronic pulsed THz systems,” Semicond. Sci. Technol. 20, S121–S127 (2005).
[Crossref]

Seidel, A.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Seo, M. A.

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).
[Crossref]

Shamonina, E.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002).
[Crossref]

Sillero, R. M.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

Solymar, L.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002).
[Crossref]

Sorolla, M.

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Taylor, A. J.

Thoman, A.

Tsai, D. P.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

van der Valk, N. C. J.

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[Crossref]

van Oosten, D.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

van Rijmenam, C. E. W. M.

P. C. M. Planken, C. E. W. M. van Rijmenam, and R. N. Schouten, “Opto-electronic pulsed THz systems,” Semicond. Sci. Technol. 20, S121–S127 (2005).
[Crossref]

Vanexter, M.

Wallauer, J.

Walther, M.

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref] [PubMed]

Whitaker, J. F.

Zentgraf, T.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Zheludev, N. I.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Bitzer and M. Walther, “Terahertz near-field imaging of metallic subwavelength holes and hole arrays,” Appl. Phys. Lett. 92, 231101 (2008).
[Crossref]

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[Crossref]

Bull. Chem. Soc. Jpn. (1)

M. Osawa, “Dynamic processes in electrochemical reactions studied by surface-enhanced infrared absorption spectroscopy (seiras),” Bull. Chem. Soc. Jpn. 70, 2861–2880 (1997).
[Crossref]

Electron. Lett. (1)

I. A. I. Al-Naib, C. Jansen, and M. Koch, “Applying the Babinet principle to asymmetric resonators,” Electron. Lett. 44, 1228–1229 (2008).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative-epsilon stopband microstrip lines based on complementary split ring resonators,” IEEE Trans. Microwave Theory Tech. 14, 280–282 (2004).

J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microwave Theory Tech. 53, 1451–1461 (2005).
[Crossref]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

J. Appl. Phys. (1)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).
[Crossref]

Opt. Express (7)

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15, 11781–11789 (2007).
[Crossref] [PubMed]

A. J. L. Adam, J. M. Brok, M. A. Seo, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. Nagel, and P. C. M. Planken, “Advanced terahertz electric near-field measurements at sub-wavelength diameter metallic apertures,” Opt. Express 16, 7407–7417 (2008).
[Crossref] [PubMed]

A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, “Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial,” Opt. Express 17, 3826–3834 (2009).
[Crossref] [PubMed]

A. Bitzer, J. Wallauer, H. Helm, H. Merbold, T. Feurer, and M. Walther, “Lattice modes mediate radiative coupling in metamaterial arrays,” Opt. Express 17, 22108–22113 (2009).
[Crossref] [PubMed]

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15, 1084–1095 (2007).
[Crossref] [PubMed]

C. C. Chen and J. F. Whitaker, “An optically-interrogated microwave-Poynting-vector sensor using cadmium manganese telluride,” Opt. Express 18, 12239–12248 (2010).
[Crossref] [PubMed]

Phys. Rev. B (1)

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Phys. Rev. Lett. (3)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref] [PubMed]

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref] [PubMed]

Science (2)

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref] [PubMed]

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326, 550–553 (2009).
[Crossref] [PubMed]

Semicond. Sci. Technol. (1)

P. C. M. Planken, C. E. W. M. van Rijmenam, and R. N. Schouten, “Opto-electronic pulsed THz systems,” Semicond. Sci. Technol. 20, S121–S127 (2005).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of the two different near-field detection techniques used in this study. (a) Photoconductive antenna as polarization sensitive near-field probe. By rotating the antenna by 90° both in-plane THz electric field components can be measured. (b) Nonlinear crystal as near-field probe. A (100)-cut ZnTe crystal allows measuring the electric out-of-plane component. In both configurations the detector is scanned together with the laser beam relative to the stationary sample in order to map the electric fields. (c) and (d) show microscope images of the investigated samples, a SRR and a CSRR, respectively.

Fig. 2
Fig. 2

Illustration of Babinet’s principle which relates the scattered fields E⃗, B⃗ and E⃗c, B⃗c behind complementary structures. SRR (a) and its complementary screen (b) illuminated by complementary incident fields.

Fig. 3
Fig. 3

FEM simulation of the field distributions around a SRR and a CSRR under complementary illumination. (a) Density plot of the in-plane magnetic near-field behind a SRR. (b,c) Streamline representation of the magnetic near-field of a SRR plotted along perpendicular cross sections through the center of the structure. (d) yz-cross section of the scattered magnetic field only, shown without superimposed driving fields. (e–h) Cross sections of the corresponding electric field distribution behind the CSRR. The color intensity scales with the amplitude of the corresponding magnetic (upper row) and electric (lower row) fields.

Fig. 4
Fig. 4

Far-field transmission spectra obtained from a 20x20 array of SRRs for two different polarizations of the incident beam relative to the sample as indicated by the insets (top curves) and corresponding spectra of the complementary sample (bottom curves). Characteristic resonances of the structures are indicated by vertical dashed lines.

Fig. 5
Fig. 5

Near-field distributions measured directly behind our samples at their lowest order resonances n=1–3. Top row: Electric in-plane (arrows) and magnetic out-of-plane (colors) field distributions behind the SRR-sample. Bottom row: Density plots of the electric out-of-plane component close to the surface of the complementary screen (CSRR). Dashed lines are indicating the positions at which the image plane intersects with the simulated xz- and yz-cross sections shown in Fig 3.

Fig. 6
Fig. 6

Near-field distributions of our structures, however, measured with interchanged detection schemes as in Fig. 5. Top row: electric near-field distribution of the out-of-plane component close to the SRR. Bottom row: electric in-plane and magnetic out-of-plane near-field distributions behind the CSRR.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E 0 c = c B 0 and B 0 c = E 0 / c ,
E c = E 0 c + c B
B c = B 0 c E / c ,
E c = c B and B c = E / c .
t + t c = 1 .

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